Strong diamagnetism for general domains and applications
Abstract
Description
We consider the Neumann Laplacian with constant magnetic field on a regular domain. Let $B$ be the strength of the magnetic field, and let $λ_1(B)$ be the first eigenvalue of the magnetic Neumann Laplacian on the domain. It is proved that $B \mapsto λ_1(B)$ is monotone increasing for large $B$. Combined with the results of \cite{FournaisHelffer3}, this implies that all the `third' critical fields for strongly Type II superconductors coincide.
A few typos corrected. One argument given in more details. Version to be published in AIF
A few typos corrected. One argument given in more details. Version to be published in AIF